Cremona's table of elliptic curves

3870 = 2 · 3² · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 43+	Signs for the Atkin-Lehner involutions
Class	3870r	Isogeny class
Conductor	3870	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	1354190400 = 26 · 39 · 52 · 43	Discriminant
Eigenvalues	2- 3- 5+ -2  2 -2  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-338,-1519]	[a1,a2,a3,a4,a6]
Generators	[-9:31:1]	Generators of the group modulo torsion
j	5841725401/1857600	j-invariant
L	4.781412204364	L(r)(E,1)/r!
Ω	1.1416580217919	Real period
R	0.34901083286301	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30960bn1 123840de1 1290f1 19350y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3870r1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	+	-2	2	-2	4	-6	-6	10	-8	2	-2	+	2	-10	-2	-12	-12	-16	16	-8	12	-6	6

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Quadratic twists for elliptic curve 3870r1

-4	8	-3	5
30960bn1	123840de1	1290f1	19350y1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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